Using \(p,q,r-\) fractional fuzzy sets ( \(p,q,r-\) FFS) to demonstrate the stability of cryptocurrencies is considered due to the complex and volatile nature of cryptocurrency markets, where traditional models may fall short in capturing nuances and uncertainties. \(p,q,r-\) FFS provides a flexible framework for modeling cryptocurrency stability by accommodating imprecise data, multidimensional analysis of various market factors, and adaptability to the unique characteristics of the cryptocurrency space, potentially offering a more comprehensive understanding of the factors influencing stability. Existing studies have explored Picture Fuzzy Sets and Spherical Fuzzy Sets, built on membership, neutrality, and non-membership grades. However, these sets can’t reach the maximum value (equal to \(1\) ) due to grade constraints. For example, when considering \(\wp =(h,\langle \text{0.9,0.8,1.0}\rangle \left|h\in H\right.)\) , these sets fall short. This is obvious when a decision-maker possesses complete confidence in an alternative, they have the option to assign a value of 1 as the assessment score for that alternative. This signifies that they harbor no doubts or uncertainties regarding the chosen option. To address this, \(p,q,r-\) Fractional Fuzzy Sets ( \(p,q,r-\) FFSs) are introduced, using new parameters \(p\) , \(q\) , and \(r\) . These parameters abide by \(p\) , \(q\ge 1\) and \(r\) as the least common multiple of \(p\) and \(q\) . We establish operational laws for \(p,q,r-\) FFSs. Based on these operational laws, we proposed a series of aggregation operators (AOs) to aggregate the information in context of \(p,q,r-\) fractional fuzzy numbers. Furthermore, we constructed a novel multi-criteria group decision-making (MCGDM) method to deal with real-world decision-making problems. A numerical example is provided to demonstrate the proposed approach.
